FIG. 1 shows an example of a conventional frequency synthesizer. In the diagram, reference numeral 1 denotes a signal generator which may be generally constituted by a crystal oscillator or constituted by a high stable device. A reference sgnal F.sub.r is output from the generator 1. An input signal from an external circuit may be also used as a reference signal. Reference numeral 2 denotes a reference signal multiplier; 3 is a mixer; 8 a fixed frequency divider; 9 a frequency phase comparator. The reference signal F.sub.r is divided into two signals. One of these signals is multiplied by L by the multiplier 2 and is input as a signal F to the mixer 3. The other signal is frequency divided into 1/M by the fixed frequency divider 8 and, thereafter, it is input as a reference signal F.sub.s to the comparator 9.
Reference numeral 4 denotes a voltage controlled oscillator (VCO); 5 a difference signal amplifier; 6 a variable frequency divider; 7 a frequency controller; and 10 a loop filter. An output signal F.sub.o of the VCO 4 is divided into two signals. One of these signals is taken out as an output of the synthesizer. The other signal is input to the mixer 3. The mixer 3 takes out a frequency F.sub.i of the difference between the output F.sub.o of the VCO 4 and the output F of the multiplier 2 and then sends it to the amplifier 5. This frequency signal is amplified by the amplifier 5 and the resultant difference signal is divided into 1/N by the variable frequency divider 6 and is input as a signal F.sub.c to the comparator 9.
The comparactor 9 compares the reference signal F.sub.s with the signal F.sub.c and outputs a voltage corresponding to the phase difference between these signals. This output is supplied to the low pass filter (loop filter) 10 which is generally constituted by an active filter. The high frequency component is removed by this filter and is input to a frequency control terminal of the VCO 4. Thus, the VCO 4 outputs a signal of the frequency corresponding to the voltage input to the frequency control terminal.
A closed loop is constituted in this manner. The output of the VCO 4 becomes a frequency signal such that the signals F.sub.c and F.sub.s finally have the same frequency and are synchronized with a constant phase difference.
Between the output frequency F.sub.o of a conventional PLL frequency synthesizer and a reference input frequency F.sub.r, there is a relation represented by either one of the following equations (1) and (2). This frequency relation is shown in FIG. 3.
In FIG. 3, solid lines indicate an example when N=3 and the relation is based on the equation (2). ##EQU1##
Therefore, by sequentially changing the value of N by "1" at one time by the controller 7, the value of F.sub.o can be changed by F.sub.r /M=F.sub.s steps.
The reason why the frequency to be divided is set to a low frequency by use of the mixer in this manner is to cope with the case where the value of F.sub.o is so high due to a microwave band or the like that a proper frequency divider cannot be obtained or where it is intended to set a value of frequency dividing ratio to a small value.
Whether the F.sub.o is expressed by the equation (1) or the equation (2) is determined by whether the output F.sub.o of the VCO 4 is set to the higher frequency or the lower frequency when there is a relation of F.sub.c &gt;F.sub.s between the input signals F.sub.c and F.sub.s of the frequency phase comparator 9. For example, when F.sub.c &gt;F.sub.s, if the output F.sub.o of the VCO 4 is set to the higher frequency, the value of F.sub.o becomes stable at the frequency expressed by the equation (1), while the value of F.sub.o becomes stable at the frequency expressed by the equation (2) if the output F.sub.o of the VCO 4 is set to the lower frequency.
The decision as to whether the output F.sub.o of the VCO 4 is set to the higher frequency or the lower frequency depends on a change in polarity of the signal passing through the comparator 9, VCO 4, and loop filter 10.
The conventional frequency synthesizer is constituted in this manner. Therefore, to change the output frequency F.sub.o within a range of a band W, the difference frequency F.sub.i must also be changed within the range of the band W, and thus the variable frequency divider 6 also needs to operate within the frequency band of W. Accordingly, there is a problem in that an expensive variable frequency divider of a wide band type is necessary to make a frequency synthesizer of a wide band type.